Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces

Marco Biroli; Umberto Mosco

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1995)

  • Volume: 6, Issue: 1, page 37-44
  • ISSN: 1120-6330

Abstract

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We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.

How to cite

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Biroli, Marco, and Mosco, Umberto. "Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 6.1 (1995): 37-44. <http://eudml.org/doc/244300>.

@article{Biroli1995,
abstract = {We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.},
author = {Biroli, Marco, Mosco, Umberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Sobolev spaces; Dirichlet forms; Degenerate elliptic operators; BV spaces; homogeneous space; degenerate elliptic operators; Sierpinski gasket; Dirichlet operators; local embedding theorems},
language = {eng},
month = {3},
number = {1},
pages = {37-44},
publisher = {Accademia Nazionale dei Lincei},
title = {Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces},
url = {http://eudml.org/doc/244300},
volume = {6},
year = {1995},
}

TY - JOUR
AU - Biroli, Marco
AU - Mosco, Umberto
TI - Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1995/3//
PB - Accademia Nazionale dei Lincei
VL - 6
IS - 1
SP - 37
EP - 44
AB - We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
LA - eng
KW - Sobolev spaces; Dirichlet forms; Degenerate elliptic operators; BV spaces; homogeneous space; degenerate elliptic operators; Sierpinski gasket; Dirichlet operators; local embedding theorems
UR - http://eudml.org/doc/244300
ER -

References

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Citations in EuDML Documents

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  1. Umberto Mosco, Variational fractals
  2. Bruno Franchi, Guozhen Lu, Richard L. Wheeden, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
  3. Bernd Kirchheim, Francesco Serra Cassano, Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group
  4. Ermanno Lanconelli, Strutture subriemanniane in alcuni problemi di Analisi
  5. Franchi, Bruno, B V spaces and rectifiability for Carnot-Carathéodory metrics: an introduction
  6. Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Trace inequalities for Carnot-Carathéodory spaces and applications

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